Demonstration and resolution of the Gibbs paradox of the first kind

TL;DR

This paper resolves the Gibbs paradox of the first kind by accounting for particle indistinguishability and correlations, showing that the paradox arises from neglecting these effects in entropy calculations.

Contribution

It provides a resolution to the Gibbs paradox by incorporating particle uncertainty and correlations, challenging previous assumptions in statistical mechanics.

Findings

The paradox is resolved by considering particle indistinguishability.

Correlations between systems affect total entropy calculations.

The resolution aligns classical and quantum statistical mechanics.

Abstract

The Gibbs paradox of the first kind (GP1) refers to the false increase in entropy which, in statistical mechanics, is calculated from the process of combining two gas systems S1 and S2 consisting of distinguishable particles. Presented in a somewhat modified form, the GP1 manifests as a contradiction to the second law of thermodynamics. Contrary to popular belief, this contradiction affects not only classical but also quantum statistical mechanics. The present paper resolves the GP1 by considering two effects: 1. The uncertainty about which particles are located in S1 and which in S2 contributes to the entropies of S1 and S2. 2. S1 and S2 are correlated by the fact that if a certain particle is located in one system, it cannot be located in the other. As a consequence, the entropy of the total system consisting of S1 and S2 is not the sum of the entropies of S1 and S2.